Does this work with negative numbers?

Yes — handles negatives correctly for modes 1 and 3. For mode 2 (X is what % of Y), if Y is negative the percentage will be negative, which is mathematically right but unusual.

Why is "decimal" useful?

Some contexts (Excel, statistics, programming) use decimals (0.225) instead of percentages (22.5%). Quick conversion for cross-tool work.

When should I use percentage points vs percent change?

They are not interchangeable. If a tax rate moves from 5% to 7%, that is a 2 percentage-point increase but a 40% relative increase. News articles routinely conflate the two — when the underlying quantity is itself a percent, always state which.

How is this different from a markup calculator?

Markup is the percent added to cost to set price (cost × (1 + markup) = price). Margin is the percent of price that is profit (price − cost) / price. They produce different numbers from the same cost / price pair — see the Markup Calculator for the dedicated tool.

Percentage Calculator

Six-mode percentage tool — X% of Y, X is what % of Y, % change, % difference (symmetric), add %, and subtract %.

Result

25% of 200

As fraction0.2500 × 200
In money$50.00

How to use this calculator

Pick the mode that matches your question.
Type the two numbers — labels adapt based on mode.
Read the primary result + secondary breakdowns.

About this tool

Six percentage problems in one tool, because most "percentage calculators" only do one. Mode 1: classic "what is 15% of $80" (the answer is $12). Mode 2: "$45 is what % of $200" (22.5%). Mode 3: percentage change between two values — useful for "stock went from $50 to $73, what %?" (+46%). Mode 4: percent difference — the order-independent variant used in scientific writing, |A−B| ÷ average × 100. Mode 5: add X% to Y — markup, sales tax, percentage raises. Mode 6: subtract X% from Y — discounts, depreciation, sale prices. Mode 3 also shows the reverse change, which is NOT the same number — going from $73 back to $50 is a 32% decrease, not 46%, because the denominators differ.

What this calculator does

This is three percentage tools in one. Mode 1 answers "what is X percent of Y" — the classic discount or tax question. Mode 2 answers "X is what percent of Y" — the share-of-whole question. Mode 3 answers "what is the percent change from A to B" and includes the reverse change, which is rarely the same number because the denominator shifts. The output includes the decimal equivalent (useful for Excel and statistics work) and a multiplier (1.46× for a 46% increase), so the same answer is presented in whichever shape your downstream workflow wants.

How it works — the formula

pct_of:   result = (X / 100) · Y
is_what:  pct    = (X / Y) · 100
change:   pct    = ((B − A) / A) · 100

Percentages are ratios scaled to a base of 100. Mode 1 is the definition. Mode 2 is the definition rearranged. Mode 3 normalises the absolute change by the starting value — and because the starting value changes between A→B and B→A, the two percent changes are different. NIST defines "percent" and "percentage point" as separate quantities; conflating them is one of the most common reporting errors in financial and statistical writing.

Sources: NIST Special Publication 811 — Guide for the Use of the International System of Units (SI), §7.10.2 on percent · Encyclopaedia Britannica — Percentage and percent change · US Bureau of Labor Statistics — Handbook of Methods (percent change conventions)

Worked examples

Example 1

Mode 1 — tip / discount

Inputs:: X = 15, Y = 80 ("what is 15% of 80?")
Output:: result = 12 (decimal 0.15 × 80)

The everyday "what is X% of Y" question — sales tax, tips, sale discounts, commissions. Mode 1 is by far the most-used percentage operation.

Example 2

Mode 2 — share-of-whole

Inputs:: X = 45, Y = 200 ("45 is what % of 200?")
Output:: 22.5%; decimal 0.225

Share-of-whole questions: market share, exam scores, conversion rates. The reciprocal is also surfaced — 200 is 444% of 45.

Example 3

Mode 3 — percent change

Inputs:: A = 50, B = 73 ("$50 stock went to $73")
Output:: +46% increase; multiplier 1.46×; reverse change −32%

Percent change is asymmetric. A +46% gain requires a −32% loss to return to start, NOT a −46% loss. This is the source of the "you lose more than you make" intuition behind sequence-of-returns risk.

The three fundamental percentage operations

Every percentage problem can be reduced to one of three basic operations. Understanding which operation applies eliminates most of the arithmetic errors people make with percentages.

1. Percent of a number (A × B/100)

What is 25% of 200? → 200 × 0.25 = 50

Multiply the base by the percentage expressed as a decimal. The result is a portion of the base.

2. Value as percent of another value (A/B × 100)

What percent is 30 of 120? → 30 ÷ 120 × 100 = 25%

Divide the first value by the second, then multiply by 100. Result is what fraction the first is of the second.

3. Percent change between two values ((B - A)/A × 100)

Price went from $80 to $95: change = (95 - 80) / 80 × 100 = 18.75%

Difference divided by original, times 100. Positive for increase, negative for decrease. The BASE is the ORIGINAL value, not the new one — critical distinction.

The percent-change trap

A common error: percent decreases and percent increases are NOT symmetric. If a $100 stock drops 50%% to $50, then rises 50%% back, it does not return to $100 — the second 50%% is applied to the new base of $50, yielding only $75. The stock needs to rise 100%% (not 50%%) to recover.

This asymmetry has major implications for investment planning. A portfolio that loses 30%% in a bear market needs to gain about 43%% just to return to breakeven, not 30%%. Volatility drag from repeated up-down cycles reduces long-term returns compared to steadier growth at the same average rate.

The formula for recovery from a percent loss: recovery gain % = loss % ÷ (1 - loss %). A 50%% loss requires 100%% gain to recover; a 25%% loss requires 33%%; a 10%% loss requires only 11%%. Losses hurt more than equal-percentage gains help.

Percentage points vs percent

One of the most consistently confused distinctions in finance and journalism: "percentage points" and "percent" are not the same. If a mortgage rate rises from 5%% to 7%%, it went up 2 percentage POINTS, but the increase is 40%% (2 / 5 = 0.4 = 40%).

Similarly, the Fed raising rates by 0.25%% typically means 25 basis points (0.25 percentage points), not a 0.25%% relative change on the current rate. This distinction matters when comparing rate changes across sources — misreading it makes rate movements sound smaller or larger than they are.

Basis points (bps): 1 basis point = 0.01 percentage point. 100 basis points = 1 percentage point. Finance professionals use basis points to avoid the percentage-vs-percentage-points confusion entirely: "The Fed raised 25 bps" is unambiguous where "The Fed raised 0.25%" is ambiguous.

Common percentage applications

Discount pricing: sale of 30%% off means new price = original × (1 - 0.30) = original × 0.70. Two stacked discounts ("30%% off, then extra 20%% off at checkout") give 0.70 × 0.80 = 0.56 = 44%% total discount, NOT 50%% — stacked discounts are always less than the sum.

Sales tax: adding 8.25%% sales tax means final price = pre-tax × 1.0825. Working backward from tax-inclusive price requires dividing by 1.0825, not multiplying by 0.9175 (which would give a wrong answer). Common error: assuming that "adding 25%%" is undone by "subtracting 25%%".

Compound growth: 5%% growth for 3 years is NOT 15%% total. Compounded, 1.05³ = 1.1576 = 15.76%% growth. For short periods and small percentages the difference is small; for long periods it is enormous. The Rule of 72 (72 ÷ growth rate = years to double) captures this compounding.

Weighted averages: percentages of different bases cannot be simply averaged. A student with 90%% in a 3-credit class and 60%% in a 4-credit class has weighted average = (90 × 3 + 60 × 4) ÷ 7 = 73%%, not 75%%.

When to use this vs other tools

Percentage Calculator is the general-purpose tool. Use a specialised calculator when the domain has its own conventions.

Markup Calculator
Use for retail / pricing — markup (percent added to cost) and margin (percent of price kept as profit) are different operations from a plain percent and have their own conventions.
Tip Calculator
Use for restaurant tipping with an n-way split. Tip is just "Mode 1 — percent of bill" plus a divide-by-n; the dedicated tool also surfaces 15/18/20% reference lines.
Inflation Calculator
Use for real-vs-nominal comparisons across years. Inflation Calculator pulls BLS CPI series, so a 1990-vs-2025 comparison uses the right cumulative percent change, not a single annual rate.
Investment Return Calculator
Use for annualised returns on multi-year investments — a single percent change over five years is not the same as a CAGR, and confusing the two is a common reporting error.

Authority note

National Institute of Standards and Technology (NIST)

Special Publication 811 — Guide for the Use of the International System of Units (SI), §7.10.2: percent

NIST SP 811 is the US authoritative reference for percent vs percentage-point usage in scientific and technical writing. The same distinction is enforced in BLS, Federal Reserve, and IMF reporting conventions.

Limitations

Percent and "percentage point" are not the same — when the underlying quantity is itself a percent (interest rate, tax rate, unemployment), always state which you mean.
Percent change is asymmetric: a +X% then −X% does not return to the start. The reverse-change line in Mode 3 makes this explicit.
Percent of negative numbers is mathematically well-defined but produces signs that may be unintuitive in the breakdown row.
For multi-period growth comparisons, an annualised (CAGR) figure is more useful than a raw single percent change — use the Investment Return Calculator instead.

This calculator is a general-purpose arithmetic tool. It does not provide financial, tax, or investment advice; check the domain-specific calculators for context-aware figures.

Frequently asked

Because the denominator changes. $100 → $150 is +50% (gain ÷ original), but $150 → $100 is -33% (loss ÷ new starting point). Mathematically symmetric only at small values.